The grades on a math midterm at Springer are normally distributed with $\mu = 82$ and $\sigma = 5.0$. Christopher earned a $69$ on the exam. Find the z-score for Christopher's exam grade. Round to two decimal places.
Answer: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Christopher's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{69 - {82}}{{5.0}}} $ ${ z \approx -2.60}$ The z-score is $-2.60$. In other words, Christopher's score was $2.60$ standard deviations below the mean.